Electronic correlationElectronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons. Within the Hartree–Fock method of quantum chemistry, the antisymmetric wave function is approximated by a single Slater determinant. Exact wave functions, however, cannot generally be expressed as single determinants.
Configuration interactionConfiguration interaction (CI) is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematically, configuration simply describes the linear combination of Slater determinants used for the wave function. In terms of a specification of orbital occupation (for instance, (1s)2(2s)2(2p)1...), interaction means the mixing (interaction) of different electronic configurations (states).
Ab initio quantum chemistry methodsAb initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term ab initio was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene. The background is described by Parr. Ab initio means "from first principles" or "from the beginning", implying that the only inputs into an ab initio calculation are physical constants.
Coupled clusterCoupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used in nuclear physics. Coupled cluster essentially takes the basic Hartree–Fock molecular orbital method and constructs multi-electron wavefunctions using the exponential cluster operator to account for electron correlation. Some of the most accurate calculations for small to medium-sized molecules use this method.
Electron configurationIn atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon atom is 1s2 2s2 2p6, meaning that the 1s, 2s and 2p subshells are occupied by 2, 2 and 6 electrons respectively. Electronic configurations describe each electron as moving independently in an orbital, in an average field created by all other orbitals.
Pearson correlation coefficientIn statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations.
CorrelationIn statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.
Intraclass correlationIn statistics, the intraclass correlation, or the intraclass correlation coefficient (ICC), is a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other. While it is viewed as a type of correlation, unlike most other correlation measures, it operates on data structured as groups rather than data structured as paired observations.
Computational chemistryComputational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of molecules, groups of molecules, and solids. It is essential because, apart from relatively recent results concerning the hydrogen molecular ion (dihydrogen cation, see references therein for more details), the quantum many-body problem cannot be solved analytically, much less in closed form.
Exchangeable random variablesIn statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered. Thus, for example the sequences both have the same joint probability distribution. It is closely related to the use of independent and identically distributed random variables in statistical models.
Multi-configurational self-consistent fieldMulti-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for molecular ground states which are quasi-degenerate with low-lying excited states or in bond-breaking situations). It uses a linear combination of configuration state functions (CSF), or configuration determinants, to approximate the exact electronic wavefunction of an atom or molecule.
Electronic band structureIn solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules.
Quantum chemistryQuantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties.
Foreign exchange reservesForeign exchange reserves (also called forex reserves or FX reserves) are cash and other reserve assets such as gold held by a central bank or other monetary authority that are primarily available to balance payments of the country, influence the foreign exchange rate of its currency, and to maintain confidence in financial markets. Reserves are held in one or more reserve currencies, nowadays mostly the United States dollar and to a lesser extent the euro.
Foreign exchange marketThe foreign exchange market (forex, FX, or currency market) is a global decentralized or over-the-counter (OTC) market for the trading of currencies. This market determines foreign exchange rates for every currency. It includes all aspects of buying, selling and exchanging currencies at current or determined prices. In terms of trading volume, it is by far the largest market in the world, followed by the credit market. The main participants in this market are the larger international banks.
Free electron modelIn solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
ColorColor (American English) or colour (Commonwealth English) is the visual perception based on the electromagnetic spectrum. Though color is not an inherent property of matter, color perception is related to an object's light absorption, reflection, emission spectra and interference. For most humans, color are perceived in the visible light spectrum with three types of cone cells (trichromacy). Other animals may have a different number of cone cell types or have eyes sensitive to different wavelength, such as bees that can distinguish ultraviolet, and thus have a different color sensitivity range.
PenA pen is a common writing instrument that applies ink to a surface, usually paper, for writing or drawing. Early pens such as reed pens, quill pens, dip pens and ruling pens held a small amount of ink on a nib or in a small void or cavity which had to be periodically recharged by dipping the tip of the pen into an inkwell. Today, such pens find only a small number of specialized uses, such as in illustration and calligraphy. Reed pens, quill pens and dip pens, which were used for writing, have been replaced by ballpoint pens, rollerball pens, fountain pens and felt or ceramic tip pens.
Color blindnessColor blindness or color vision deficiency (CVD) is the decreased ability to see color or differences in color. It can impair tasks such as selecting ripe fruit, choosing clothing, and reading traffic lights. Color blindness may make some academic activities more difficult. However, issues are generally minor, and people with colorblindness automatically develop adaptations and coping mechanisms. People with total color blindness (achromatopsia) may also be uncomfortable in bright environments and have decreased visual acuity.
Primary colorA set of primary colors or primary colours (see spelling differences) consists of colorants or colored lights that can be mixed in varying amounts to produce a gamut of colors. This is the essential method used to create the perception of a broad range of colors in, e.g., electronic displays, color printing, and paintings. Perceptions associated with a given combination of primary colors can be predicted by an appropriate mixing model (e.g., additive, subtractive) that reflects the physics of how light interacts with physical media, and ultimately the retina.
